A note on downdating the Cholesky factorization
95. A. W. Bojanczyk, R. P. Brent, P. Van Dooren and F. R. de Hoog,
A note on downdating the Cholesky factorization,
SIAM J. Scientific and Statistical Computing 8 (1987), 210-221.
A modified version appeared in
Algorithms and Applications on Vector and Parallel Computers,
Elsevier, Amsterdam, 1987, 307-323.
MR 89i:65042, 89f:65002.
Paper: pdf (815K).
We analyse and compare three algorithms for "downdating" the Cholesky
factorization of a positive definite matrix.
Although the algorithms are closely related, their numerical properties
differ. Two algorithms are stable in a certain "mixed" sense while the
other is unstable. In addition to comparing the numerical properties of
the algorithms, we compare their computational complexity and their
suitability for implementation on parallel or vector computers.
For an application of downdating to the QR factorization of Toeplitz
matrices, see .
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